发表机构
Aalto University（阿尔托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究系统阐明了非复发性流行病模型映射到键渗流的适用条件，提出了同构、边际感染概率相等和预期规模相等三种等价形式，并通过数值验证确立了该方法的理论基础与局限。
AI 中文摘要
复杂网络上的非复发性流行病，例如典型的易感-感染-恢复（SIR）模型，通常通过将该模型映射到键渗流来研究。然而，这种映射成立的条件下，除特定情况外，尚未被完全理解。在此，我们从流行病模型和底层网络的最小假设出发，系统地确定该映射何时可以应用。具体而言，我们讨论了一般非复发性流行病模型与伯努利键渗流之间三种不同等价形式成立的条件：同构、边际感染概率相等以及预期流行病规模相等。我们通过数值实验证明了我们发现的正确性，并考察了当这些等价关系不成立时流行病学结果受到的影响。我们的结果为分析网络上流行病过程的常用工具建立了方法论基础，并明确了其局限性。
英文摘要
Non-recurrent epidemics on complex networks, such as the paradigmatic susceptible-infected-recovered (SIR) model, are often studied by mapping the model to bond percolation. However, the conditions under which this identification is justified have not been fully understood, except in specific cases. Here, we systematically determine when this mapping can be applied, starting from minimal assumptions on the epidemic model and the underlying network. Specifically, we discuss the conditions for three different forms of equivalence between a general non-recurrent epidemic model and Bernoulli bond percolation: isomorphism, equality of marginal infection probabilities, and equality of expected epidemic size. We numerically demonstrate the validity of our findings and examine how epidemiological outcomes are affected when these equivalences are not upheld. Our results establish the methodological basis and limitations of a common tool for analyzing epidemic processes on networks.
